Related papers: Universality in quantum chaos and the one paramete…
We analyze numerically ensembles of tight-binding Hamiltonians describing highly-symmetric graphene nanoflakes with weak diagonal disorder induced by random electrostatic potential landscapes. When increasing the disorder strength,…
We prove a generalized fluctuation-dissipation theorem for a certain class of out-of-time-ordered correlators (OTOCs) with a modified statistical average, which we call bipartite OTOCs, for general quantum systems in thermal equilibrium.…
Matter exhibits phases and their transitions. These transitions are classified as first-order phase transitions (FOPTs) and continuous ones. While the latter has a well-established theory of the renormalization group, the former is only…
Matter exhibits phases and their transitions. These transitions are classified as first-order phase transitions (FOPTs) and continuous ones. While the latter has a well-established theory of the renormalization group, the former is only…
We explore the concept of scaling invariance in a type of dynamical systems that undergo a transition from order (regularity) to disorder (chaos). The systems are described by a two-dimensional, nonlinear mapping that preserves the area in…
Scaling properties of the quantum Hall metal-insulator transition are severely affected by finite size effects in small systems. Surprisingly, despite the narrow spatial range where probability structure functions exhibit multifractal…
In recent years, the investigation of chaos has become a bridge connecting gravity theory and quantum field theory, especially within the framework of gauge-gravity duality. In this work, we study holographically the chaos in the matrix…
A new universality class distinct from the standard Wigner-Dyson ones is identified. This class is realized by putting a metallic quantum dot in contact with a superconductor, while applying a magnetic field so as to make the pairing field…
We develop a statistical theory that describes quantum-mechanical scattering of a particle by a cavity when the geometry is such that the classical dynamics is chaotic. This picture is relevant to a variety of physical systems, ranging from…
The universality of the metal-insulator transition in three-dimensional disordered system is confirmed by numerical analysis of the scaling properties of the electronic wave functions. We prove that the critical exponent $\nu$ and the…
Recent years have seen an increasing interest in quantum chaos and related aspects of spatially extended systems, such as spin chains. However, the results are strongly system dependent, generic approaches suggest the presence of many-body…
Systems undergoing an equilibrium phase transition from a liquid state to an amorphous solid state exhibit certain universal characteristics. Chief among these are the fraction of particles that are randomly localized and the scaling…
We consider orthogonal, unitary, and symplectic ensembles of random matrices with (1/a)(ln x)^2 potentials, which obey spectral statistics different from the Wigner-Dyson and are argued to have multifractal eigenstates. If the coefficient…
We consider universal aspects of two problems: (i) the slow purification of a large number of qubits by repeated quantum measurements, and (ii) the singular value structure of a product ${m_t m_{t-1}\ldots m_1}$ of many large random…
The disorder induced metal--insulator transition is investigated in a three-dimensional simple cubic lattice and compared for the presence and absence of time-reversal and spin-rotational symmetry, i.e. in the three conventional symmetry…
We elucidate the basic physical mechanisms responsible for the quantum-classical transition in one-dimensional, bounded chaotic systems subject to unconditioned environmental interactions. We show that such a transition occurs due to the…
The emergence of random matrix spectral correlations in interacting quantum systems is a defining feature of quantum chaos. We study such correlations in terms of the spectral form factor and its moments in interacting chaotic few- and…
The mapping between the metal-insulator transition of the quantum Hall system and a superfluid-to-insulator transition is revisited based on a disordered anyon model. The one-parameter scaling of the superfluid-to-insulator transition is…
We discuss the universal scaling laws of order parameter fluctuations in any system in which the second-order critical behaviour can be identified. These scaling laws can be derived rigorously for equilibrium systems when combined with the…
Phase transitions and critical phenomena are among the most intriguing phenomena in nature and society. They are classified as first-order phase transitions (FOPTs) and continuous ones. While the latter show marvelous phenomena of scaling…